/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.pl # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern f(g,g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToIRSwTTransformerProof [SOUND, 99 ms] (2) IRSwT (3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms] (4) IRSwT (5) IntTRSCompressionProof [EQUIVALENT, 56 ms] (6) IRSwT (7) IRSFormatTransformerProof [EQUIVALENT, 0 ms] (8) IRSwT (9) IRSwTTerminationDigraphProof [EQUIVALENT, 72 ms] (10) IRSwT (11) IntTRSCompressionProof [EQUIVALENT, 0 ms] (12) IRSwT (13) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms] (14) IRSwT (15) TempFilterProof [SOUND, 37 ms] (16) IntTRS (17) PolynomialOrderProcessor [EQUIVALENT, 12 ms] (18) YES ---------------------------------------- (0) Obligation: Clauses: f(X, Y) :- loop(X, Y, 1, 0). loop(X, Y, Flag, C) :- ','(=:=(Flag, 1), ','(<(X, Y), ','(is(Flag1, 1), ','(is(X1, +(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, Flag1, C1)))))). loop(X, Y, Flag, C) :- ','(=:=(Flag, 1), ','(>(X, Y), ','(is(Flag1, 0), ','(is(X1, +(X, 1)), ','(is(C1, +(C, 1)), loop(X1, Y, Flag1, C1)))))). loop(X, Y, Flag, C) :- =\=(Flag, 1). Query: f(g,g) ---------------------------------------- (1) PrologToIRSwTTransformerProof (SOUND) Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert { "root": 2, "program": { "directives": [], "clauses": [ [ "(f X Y)", "(loop X Y (1) (0))" ], [ "(loop X Y Flag C)", "(',' (=:= Flag (1)) (',' (< X Y) (',' (is Flag1 (1)) (',' (is X1 (+ X (1))) (',' (is C1 (+ C (1))) (loop X1 Y Flag1 C1))))))" ], [ "(loop X Y Flag C)", "(',' (=:= Flag (1)) (',' (> X Y) (',' (is Flag1 (0)) (',' (is X1 (+ X (1))) (',' (is C1 (+ C (1))) (loop X1 Y Flag1 C1))))))" ], [ "(loop X Y Flag C)", "(=\\= Flag (1))" ] ] }, "graph": { "nodes": { "3081": { "goal": [{ "clause": -1, "scope": -1, "term": "(loop T78 T74 T77 T79)" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [ { "lhs": { "type": "PlainIntegerConstant", "value": "1" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "1" }, "operation": "=" }, { "lhs": { "name": "T23", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "1" }, 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"PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T108", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "1" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "1" }, "operation": "=" }, { "lhs": { "type": "PlainIntegerConstant", "value": "0" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "0" }, "operation": "=" }, { "lhs": { "arguments": [ { "name": "T104", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "name": "T104", "type": "PlainIntegerVariable" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "type": "PlainIntegerRelation", "rhs": { "arguments": [ { "type": "PlainIntegerConstant", "value": "0" }, { "type": "PlainIntegerConstant", "value": "1" } ], "type": "PlainIntegerOperation", "operation": "+" }, "operation": "=" }, { "lhs": { "name": "T105", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T104", "type": "PlainIntegerVariable" }, "operation": "<" }, { "lhs": { "name": "T104", "type": "PlainIntegerVariable" }, "type": "PlainIntegerRelation", "rhs": { "name": "T104", "type": "PlainIntegerVariable" }, "operation": "<" } ] }, "ground": ["T163"], "free": [], "exprvars": [ "T104", "T164", "T105", "T162", "T106", "T161", "T108", "T163", "T107" ] } }, "628": { "goal": [{ "clause": -1, "scope": -1, "term": "(',' (< T21 T22) (',' (is X48 (1)) (',' (is X49 (+ T21 (1))) (',' (is X50 (+ (0) (1))) (loop X49 T22 X48 X50)))))" }], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [{ "lhs": { "type": "PlainIntegerConstant", "value": "1" }, "type": "PlainIntegerRelation", "rhs": { "type": "PlainIntegerConstant", "value": "1" }, "operation": "=" }] }, "ground": [ "T22", "T21" ], "free": [ "X48", "X49", "X50" ], "exprvars": [] } }, "629": { "goal": [], "kb": { "nonunifying": [], "intvars": {}, "arithmetic": { "type": "PlainIntegerRelationState", "relations": [] }, "ground": [], "free": [], "exprvars": [] } } }, "edges": [ { "from": 2, "to": 5, "label": "CASE" }, { "from": 5, "to": 13, "label": "ONLY EVAL with clause\nf(X13, X14) :- loop(X13, X14, 1, 0).\nand substitutionT1 -> T9,\nX13 -> T9,\nT2 -> T10,\nX14 -> T10" }, { "from": 13, "to": 14, "label": "CASE" }, { "from": 14, "to": 16, "label": "PARALLEL" }, { "from": 14, "to": 17, "label": "PARALLEL" }, { "from": 16, "to": 18, "label": "ONLY EVAL with clause\nloop(X44, X45, X46, X47) :- ','(=:=(X46, 1), ','(<(X44, X45), ','(is(X48, 1), ','(is(X49, +(X44, 1)), ','(is(X50, +(X47, 1)), loop(X49, X45, X48, X50)))))).\nand substitutionT9 -> T21,\nX44 -> T21,\nT10 -> T22,\nX45 -> T22,\nX46 -> 1,\nX47 -> 0" }, { "from": 17, "to": 3102, "label": "PARALLEL" }, { "from": 17, "to": 3103, "label": "PARALLEL" }, { "from": 18, "to": 628, "label": "ARITHCOMP SUCCESS" }, { "from": 628, "to": 629, "label": "IS ERROR" }, { "from": 628, "to": 777, "label": "ARITHCOMP SUCCESS" }, { "from": 628, "to": 778, "label": "ARITHCOMP FAIL" }, { "from": 777, "to": 779, "label": "\nX48 -> T23" }, { "from": 779, "to": 780, "label": "\nX49 -> T24" }, { "from": 780, "to": 831, "label": "\nX50 -> T25" }, { "from": 831, "to": 832, "label": "CASE" }, { "from": 832, "to": 1350, "label": "PARALLEL" }, { "from": 832, "to": 1351, "label": "PARALLEL" }, { "from": 1350, "to": 1352, "label": "ONLY EVAL with clause\nloop(X80, X81, X82, X83) :- ','(=:=(X82, 1), ','(<(X80, X81), ','(is(X84, 1), ','(is(X85, +(X80, 1)), ','(is(X86, +(X83, 1)), loop(X85, X81, X84, X86)))))).\nand substitutionT24 -> T46,\nX80 -> T46,\nT22 -> T47,\nX81 -> T47,\nT23 -> T48,\nX82 -> T48,\nT25 -> T49,\nX83 -> T49" }, { "from": 1351, "to": 3004, "label": "PARALLEL" }, { "from": 1351, "to": 3005, "label": "PARALLEL" }, { "from": 1352, "to": 2703, "label": "ARITHCOMP SUCCESS" }, { "from": 1352, "to": 2704, "label": "ARITHCOMP FAIL" }, { "from": 2703, "to": 2990, "label": "ARITHCOMP SUCCESS" }, { "from": 2703, "to": 2991, "label": "ARITHCOMP FAIL" }, { "from": 2990, "to": 2992, "label": "\nX84 -> T50" }, { "from": 2992, "to": 2993, "label": "\nX85 -> T51" }, { "from": 2993, "to": 2994, "label": "\nX86 -> T52" }, { "from": 2994, "to": 831, "label": "INSTANCE with matching:\nT24 -> T51\nT22 -> T47\nT23 -> T50\nT25 -> T52\nX48 -> X84\nX49 -> X85\nX50 -> X86" }, { "from": 3004, "to": 3006, "label": "ONLY EVAL with clause\nloop(X116, X117, X118, X119) :- ','(=:=(X118, 1), ','(>(X116, X117), ','(is(X120, 0), ','(is(X121, +(X116, 1)), ','(is(X122, +(X119, 1)), loop(X121, X117, X120, X122)))))).\nand substitutionT24 -> T73,\nX116 -> T73,\nT22 -> T74,\nX117 -> T74,\nT23 -> T75,\nX118 -> T75,\nT25 -> T76,\nX119 -> T76" }, { "from": 3005, "to": 3089, "label": "ONLY EVAL with clause\nloop(X138, X139, X140, X141) :- =\\=(X140, 1).\nand substitutionT24 -> T92,\nX138 -> T92,\nT22 -> T93,\nX139 -> T93,\nT23 -> T94,\nX140 -> T94,\nT25 -> T95,\nX141 -> T95" }, { "from": 3006, "to": 3065, "label": "ARITHCOMP SUCCESS" }, { "from": 3006, "to": 3066, "label": "ARITHCOMP FAIL" }, { "from": 3065, "to": 3077, "label": "ARITHCOMP SUCCESS" }, { "from": 3065, "to": 3078, "label": "ARITHCOMP FAIL" }, { "from": 3077, "to": 3079, "label": "\nX120 -> T77" }, { "from": 3079, "to": 3080, "label": "\nX121 -> T78" }, { "from": 3080, "to": 3081, "label": "\nX122 -> T79" }, { "from": 3081, "to": 831, "label": "INSTANCE with matching:\nT24 -> T78\nT22 -> T74\nT23 -> T77\nT25 -> T79\nX48 -> X120\nX49 -> X121\nX50 -> X122" }, { "from": 3089, "to": 3091, "label": "ARITHCOMP SUCCESS" }, { "from": 3089, "to": 3092, "label": "ARITHCOMP FAIL" }, { "from": 3091, "to": 3093, "label": "SUCCESS" }, { "from": 3102, "to": 3106, "label": "ONLY EVAL with clause\nloop(X164, X165, X166, X167) :- ','(=:=(X166, 1), ','(>(X164, X165), ','(is(X168, 0), ','(is(X169, +(X164, 1)), ','(is(X170, +(X167, 1)), loop(X169, X165, X168, X170)))))).\nand substitutionT9 -> T104,\nX164 -> T104,\nT10 -> T105,\nX165 -> T105,\nX166 -> 1,\nX167 -> 0" }, { "from": 3103, "to": 3473, "label": "ONLY EVAL with clause\nloop(X256, X257, X258, X259) :- =\\=(X258, 1).\nand substitutionT9 -> T169,\nX256 -> T169,\nT10 -> T170,\nX257 -> T170,\nX258 -> 1,\nX259 -> 0" }, { "from": 3106, "to": 3111, "label": "ARITHCOMP SUCCESS" }, { "from": 3111, "to": 3112, "label": "IS ERROR" }, { "from": 3111, "to": 3219, "label": "ARITHCOMP SUCCESS" }, { "from": 3111, "to": 3220, "label": "ARITHCOMP FAIL" }, { "from": 3219, "to": 3221, "label": "\nX168 -> T106" }, { "from": 3221, "to": 3222, "label": "\nX169 -> T107" }, { "from": 3222, "to": 3223, "label": "\nX170 -> T108" }, { "from": 3223, "to": 3332, "label": "CASE" }, { "from": 3332, "to": 3333, "label": "PARALLEL" }, { "from": 3332, "to": 3334, "label": "PARALLEL" }, { "from": 3333, "to": 3335, "label": "ONLY EVAL with clause\nloop(X200, X201, X202, X203) :- ','(=:=(X202, 1), ','(<(X200, X201), ','(is(X204, 1), ','(is(X205, +(X200, 1)), ','(is(X206, +(X203, 1)), loop(X205, X201, X204, X206)))))).\nand substitutionT107 -> T129,\nX200 -> T129,\nT105 -> T130,\nX201 -> T130,\nT106 -> T131,\nX202 -> T131,\nT108 -> T132,\nX203 -> T132" }, { "from": 3334, "to": 3419, "label": "PARALLEL" }, { "from": 3334, "to": 3420, "label": "PARALLEL" }, { "from": 3419, "to": 3421, "label": "ONLY EVAL with clause\nloop(X229, X230, X231, X232) :- ','(=:=(X231, 1), ','(>(X229, X230), ','(is(X233, 0), ','(is(X234, +(X229, 1)), ','(is(X235, +(X232, 1)), loop(X234, X230, X233, X235)))))).\nand substitutionT107 -> T149,\nX229 -> T149,\nT105 -> T150,\nX230 -> T150,\nT106 -> T151,\nX231 -> T151,\nT108 -> T152,\nX232 -> T152" }, { "from": 3420, "to": 3465, "label": "ONLY EVAL with clause\nloop(X244, X245, X246, X247) :- =\\=(X246, 1).\nand substitutionT107 -> T161,\nX244 -> T161,\nT105 -> T162,\nX245 -> T162,\nT106 -> T163,\nX246 -> T163,\nT108 -> T164,\nX247 -> T164" }, { "from": 3473, "to": 3802, "label": "ARITHCOMP FAIL" } ], "type": "Graph" } } ---------------------------------------- (2) Obligation: Rules: f2994_out(T51, T47, T50, T52, T46, T49, T48) -> f2993_out(T49, T51, T47, T50, T46, T48) :|: TRUE f2993_in(x, x1, x2, x3, x4, x5) -> f2994_in(x1, x2, x3, x6, x4, x, x5) :|: x6 = x + 1 f3079_in(T73, T76, T74, T77, T75) -> f3080_in(T76, T78, T74, T77, T75, T73) :|: T78 = T73 + 1 f3080_out(x7, x8, x9, x10, x11, x12) -> f3079_out(x12, x7, x9, x10, x11) :|: TRUE f2990_out(x13, x14, x15, x16) -> f2703_out(x13, x15, x14, x16) :|: x13 < x15 f2703_in(x17, x18, x19, x20) -> f2991_in(x18, x17, x19, x20) :|: x17 >= x18 f2703_in(x21, x22, x23, x24) -> f2990_in(x21, x23, x22, x24) :|: x21 < x22 f2991_out(x25, x26, x27, x28) -> f2703_out(x26, x25, x27, x28) :|: x26 >= x25 f3077_out(x29, x30, x31, x32) -> f3065_out(x29, x31, x30, x32) :|: x29 > x31 f3065_in(x33, x34, x35, x36) -> f3078_in(x36, x34, x33, x35) :|: x33 <= x34 f3078_out(x37, x38, x39, x40) -> f3065_out(x39, x38, x40, x37) :|: x39 <= x38 f3065_in(x41, x42, x43, x44) -> f3077_in(x41, x43, x42, x44) :|: x41 > x42 f3081_in(x45, x46, x47, x48, x49, x50, x51) -> f831_in(x45, x46, x47, x48, x52) :|: TRUE f831_out(x53, x54, x55, x56, x57) -> f3081_out(x53, x54, x55, x56, x58, x59, x60) :|: TRUE f1350_in(x61, x62, x63, x64) -> f1352_in(x63, x61, x62, x64) :|: TRUE f1352_out(x65, x66, x67, x68) -> f1350_out(x66, x67, x65, x68) :|: TRUE f831_in(T24, T22, T23, T25, T21) -> f832_in(T24, T22, T23, T25) :|: TRUE f832_out(x69, x70, x71, x72) -> f831_out(x69, x70, x71, x72, x73) :|: TRUE f3065_out(x74, x75, x76, x77) -> f3006_out(x77, x74, x75, x76) :|: x77 = 1 f3006_in(x78, x79, x80, x81) -> f3065_in(x79, x80, x81, x78) :|: x78 = 1 f3066_out(x82, x83, x84, x85) -> f3006_out(x82, x84, x83, x85) :|: !(x82 = 1) f3006_in(x86, x87, x88, x89) -> f3066_in(x86, x88, x87, x89) :|: !(x86 = 1) f831_out(x90, x91, x92, x93, x94) -> f2994_out(x90, x91, x92, x93, x95, x96, x97) :|: TRUE f2994_in(x98, x99, x100, x101, x102, x103, x104) -> f831_in(x98, x99, x100, x101, x105) :|: TRUE f3080_in(x106, x107, x108, x109, x110, x111) -> f3081_in(x107, x108, x109, x112, x110, x111, x106) :|: x112 = x106 + 1 f3081_out(x113, x114, x115, x116, x117, x118, x119) -> f3080_out(x119, x113, x114, x115, x117, x118) :|: TRUE f3006_out(x120, x121, x122, x123) -> f3004_out(x121, x122, x120, x123) :|: TRUE f3004_in(x124, x125, x126, x127) -> f3006_in(x126, x124, x125, x127) :|: TRUE f2992_in(x128, x129, x130, x131, x132) -> f2993_in(x129, x133, x130, x131, x128, x132) :|: x133 = x128 + 1 f2993_out(x134, x135, x136, x137, x138, x139) -> f2992_out(x138, x134, x136, x137, x139) :|: TRUE f1351_in(x140, x141, x142, x143) -> f3004_in(x140, x141, x142, x143) :|: TRUE f3005_out(x144, x145, x146, x147) -> f1351_out(x144, x145, x146, x147) :|: TRUE f3004_out(x148, x149, x150, x151) -> f1351_out(x148, x149, x150, x151) :|: TRUE f1351_in(x152, x153, x154, x155) -> f3005_in(x152, x153, x154, x155) :|: TRUE f2990_in(x156, x157, x158, x159) -> f2992_in(x156, x157, x158, x160, x159) :|: x160 = 1 f2992_out(x161, x162, x163, x164, x165) -> f2990_out(x161, x162, x163, x165) :|: TRUE f3077_in(x166, x167, x168, x169) -> f3079_in(x166, x167, x168, x170, x169) :|: x170 = 0 f3079_out(x171, x172, x173, x174, x175) -> f3077_out(x171, x172, x173, x175) :|: TRUE f1350_out(x176, x177, x178, x179) -> f832_out(x176, x177, x178, x179) :|: TRUE f832_in(x180, x181, x182, x183) -> f1350_in(x180, x181, x182, x183) :|: TRUE f1351_out(x184, x185, x186, x187) -> f832_out(x184, x185, x186, x187) :|: TRUE f832_in(x188, x189, x190, x191) -> f1351_in(x188, x189, x190, x191) :|: TRUE f2703_out(x192, x193, x194, x195) -> f1352_out(x195, x192, x193, x194) :|: x195 = 1 f1352_in(x196, x197, x198, x199) -> f2703_in(x197, x198, x199, x196) :|: x196 = 1 f2704_out(x200, x201, x202, x203) -> f1352_out(x203, x201, x200, x202) :|: !(x203 = 1) f1352_in(x204, x205, x206, x207) -> f2704_in(x206, x205, x207, x204) :|: !(x204 = 1) f5_out(T1, T2) -> f2_out(T1, T2) :|: TRUE f2_in(x208, x209) -> f5_in(x208, x209) :|: TRUE f13_out(T9, T10) -> f5_out(T9, T10) :|: TRUE f5_in(x210, x211) -> f13_in(x210, x211) :|: TRUE f13_in(x212, x213) -> f14_in(x212, x213) :|: TRUE f14_out(x214, x215) -> f13_out(x214, x215) :|: TRUE f17_out(x216, x217) -> f14_out(x216, x217) :|: TRUE f14_in(x218, x219) -> f16_in(x218, x219) :|: TRUE f14_in(x220, x221) -> f17_in(x220, x221) :|: TRUE f16_out(x222, x223) -> f14_out(x222, x223) :|: TRUE f18_out(x224, x225) -> f16_out(x224, x225) :|: TRUE f16_in(x226, x227) -> f18_in(x226, x227) :|: TRUE f628_out(x228, x229) -> f18_out(x228, x229) :|: 1 = 1 f18_in(x230, x231) -> f628_in(x230, x231) :|: 1 = 1 f778_out(x232, x233) -> f628_out(x233, x232) :|: x233 >= x232 f628_in(x234, x235) -> f778_in(x235, x234) :|: x234 >= x235 f629_out -> f628_out(x236, x237) :|: TRUE f628_in(x238, x239) -> f777_in(x238, x239) :|: x238 < x239 f628_in(x240, x241) -> f629_in :|: TRUE f777_out(x242, x243) -> f628_out(x242, x243) :|: x242 < x243 f777_in(x244, x245) -> f779_in(x244, x245, x246) :|: x246 = 1 f779_out(x247, x248, x249) -> f777_out(x247, x248) :|: TRUE f780_out(x250, x251, x252, x253) -> f779_out(x253, x251, x252) :|: TRUE f779_in(x254, x255, x256) -> f780_in(x257, x255, x256, x254) :|: x257 = x254 + 1 f780_in(x258, x259, x260, x261) -> f831_in(x258, x259, x260, x262, x261) :|: x262 = 0 + 1 f831_out(x263, x264, x265, x266, x267) -> f780_out(x263, x264, x265, x267) :|: TRUE Start term: f2_in(T1, T2) ---------------------------------------- (3) IRSwTSimpleDependencyGraphProof (EQUIVALENT) Constructed simple dependency graph. Simplified to the following IRSwTs: intTRSProblem: f2993_in(x, x1, x2, x3, x4, x5) -> f2994_in(x1, x2, x3, x6, x4, x, x5) :|: x6 = x + 1 f3079_in(T73, T76, T74, T77, T75) -> f3080_in(T76, T78, T74, T77, T75, T73) :|: T78 = T73 + 1 f2703_in(x21, x22, x23, x24) -> f2990_in(x21, x23, x22, x24) :|: x21 < x22 f3065_in(x41, x42, x43, x44) -> f3077_in(x41, x43, x42, x44) :|: x41 > x42 f3081_in(x45, x46, x47, x48, x49, x50, x51) -> f831_in(x45, x46, x47, x48, x52) :|: TRUE f1350_in(x61, x62, x63, x64) -> f1352_in(x63, x61, x62, x64) :|: TRUE f831_in(T24, T22, T23, T25, T21) -> f832_in(T24, T22, T23, T25) :|: TRUE f3006_in(x78, x79, x80, x81) -> f3065_in(x79, x80, x81, x78) :|: x78 = 1 f2994_in(x98, x99, x100, x101, x102, x103, x104) -> f831_in(x98, x99, x100, x101, x105) :|: TRUE f3080_in(x106, x107, x108, x109, x110, x111) -> f3081_in(x107, x108, x109, x112, x110, x111, x106) :|: x112 = x106 + 1 f3004_in(x124, x125, x126, x127) -> f3006_in(x126, x124, x125, x127) :|: TRUE f2992_in(x128, x129, x130, x131, x132) -> f2993_in(x129, x133, x130, x131, x128, x132) :|: x133 = x128 + 1 f1351_in(x140, x141, x142, x143) -> f3004_in(x140, x141, x142, x143) :|: TRUE f2990_in(x156, x157, x158, x159) -> f2992_in(x156, x157, x158, x160, x159) :|: x160 = 1 f3077_in(x166, x167, x168, x169) -> f3079_in(x166, x167, x168, x170, x169) :|: x170 = 0 f832_in(x180, x181, x182, x183) -> f1350_in(x180, x181, x182, x183) :|: TRUE f832_in(x188, x189, x190, x191) -> f1351_in(x188, x189, x190, x191) :|: TRUE f1352_in(x196, x197, x198, x199) -> f2703_in(x197, x198, x199, x196) :|: x196 = 1 ---------------------------------------- (4) Obligation: Rules: f2993_in(x, x1, x2, x3, x4, x5) -> f2994_in(x1, x2, x3, x6, x4, x, x5) :|: x6 = x + 1 f3079_in(T73, T76, T74, T77, T75) -> f3080_in(T76, T78, T74, T77, T75, T73) :|: T78 = T73 + 1 f2703_in(x21, x22, x23, x24) -> f2990_in(x21, x23, x22, x24) :|: x21 < x22 f3065_in(x41, x42, x43, x44) -> f3077_in(x41, x43, x42, x44) :|: x41 > x42 f3081_in(x45, x46, x47, x48, x49, x50, x51) -> f831_in(x45, x46, x47, x48, x52) :|: TRUE f1350_in(x61, x62, x63, x64) -> f1352_in(x63, x61, x62, x64) :|: TRUE f831_in(T24, T22, T23, T25, T21) -> f832_in(T24, T22, T23, T25) :|: TRUE f3006_in(x78, x79, x80, x81) -> f3065_in(x79, x80, x81, x78) :|: x78 = 1 f2994_in(x98, x99, x100, x101, x102, x103, x104) -> f831_in(x98, x99, x100, x101, x105) :|: TRUE f3080_in(x106, x107, x108, x109, x110, x111) -> f3081_in(x107, x108, x109, x112, x110, x111, x106) :|: x112 = x106 + 1 f3004_in(x124, x125, x126, x127) -> f3006_in(x126, x124, x125, x127) :|: TRUE f2992_in(x128, x129, x130, x131, x132) -> f2993_in(x129, x133, x130, x131, x128, x132) :|: x133 = x128 + 1 f1351_in(x140, x141, x142, x143) -> f3004_in(x140, x141, x142, x143) :|: TRUE f2990_in(x156, x157, x158, x159) -> f2992_in(x156, x157, x158, x160, x159) :|: x160 = 1 f3077_in(x166, x167, x168, x169) -> f3079_in(x166, x167, x168, x170, x169) :|: x170 = 0 f832_in(x180, x181, x182, x183) -> f1350_in(x180, x181, x182, x183) :|: TRUE f832_in(x188, x189, x190, x191) -> f1351_in(x188, x189, x190, x191) :|: TRUE f1352_in(x196, x197, x198, x199) -> f2703_in(x197, x198, x199, x196) :|: x196 = 1 ---------------------------------------- (5) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (6) Obligation: Rules: f832_in(x180:0, x181:0, cons_1, x183:0) -> f832_in(x180:0 + 1, x181:0, 1, x183:0 + 1) :|: x181:0 > x180:0 && cons_1 = 1 f832_in(x, x1, x2, x3) -> f832_in(x + 1, x1, 0, x3 + 1) :|: x1 < x && x2 = 1 ---------------------------------------- (7) IRSFormatTransformerProof (EQUIVALENT) Reformatted IRS to match normalized format (transformed away non-linear left-hand sides, !=, / and %). ---------------------------------------- (8) Obligation: Rules: f832_in(x180:0, x181:0, cons_1, x183:0) -> f832_in(arith, x181:0, 1, arith1) :|: x181:0 > x180:0 && cons_1 = 1 && arith = x180:0 + 1 && arith1 = x183:0 + 1 f832_in(x4, x5, x6, x7) -> f832_in(x8, x5, 0, x9) :|: x5 < x4 && x6 = 1 && x8 = x4 + 1 && x9 = x7 + 1 ---------------------------------------- (9) IRSwTTerminationDigraphProof (EQUIVALENT) Constructed termination digraph! Nodes: (1) f832_in(x180:0, x181:0, cons_1, x183:0) -> f832_in(arith, x181:0, 1, arith1) :|: x181:0 > x180:0 && cons_1 = 1 && arith = x180:0 + 1 && arith1 = x183:0 + 1 (2) f832_in(x4, x5, x6, x7) -> f832_in(x8, x5, 0, x9) :|: x5 < x4 && x6 = 1 && x8 = x4 + 1 && x9 = x7 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (10) Obligation: Termination digraph: Nodes: (1) f832_in(x180:0, x181:0, cons_1, x183:0) -> f832_in(arith, x181:0, 1, arith1) :|: x181:0 > x180:0 && cons_1 = 1 && arith = x180:0 + 1 && arith1 = x183:0 + 1 Arcs: (1) -> (1) This digraph is fully evaluated! ---------------------------------------- (11) IntTRSCompressionProof (EQUIVALENT) Compressed rules. ---------------------------------------- (12) Obligation: Rules: f832_in(x180:0:0, x181:0:0, cons_1, x183:0:0) -> f832_in(x180:0:0 + 1, x181:0:0, 1, x183:0:0 + 1) :|: x181:0:0 > x180:0:0 && cons_1 = 1 ---------------------------------------- (13) IntTRSUnneededArgumentFilterProof (EQUIVALENT) Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements: f832_in(x1, x2, x3, x4) -> f832_in(x1, x2, x3) ---------------------------------------- (14) Obligation: Rules: f832_in(x180:0:0, x181:0:0, cons_1) -> f832_in(x180:0:0 + 1, x181:0:0, 1) :|: x181:0:0 > x180:0:0 && cons_1 = 1 ---------------------------------------- (15) TempFilterProof (SOUND) Used the following sort dictionary for filtering: f832_in(INTEGER, INTEGER, VARIABLE) Replaced non-predefined constructor symbols by 0. ---------------------------------------- (16) Obligation: Rules: f832_in(x180:0:0, x181:0:0, c) -> f832_in(c1, x181:0:0, c2) :|: c2 = 1 && (c1 = x180:0:0 + 1 && c = 1) && (x181:0:0 > x180:0:0 && cons_1 = 1) ---------------------------------------- (17) PolynomialOrderProcessor (EQUIVALENT) Found the following polynomial interpretation: [f832_in(x, x1, x2)] = -x + x1 The following rules are decreasing: f832_in(x180:0:0, x181:0:0, c) -> f832_in(c1, x181:0:0, c2) :|: c2 = 1 && (c1 = x180:0:0 + 1 && c = 1) && (x181:0:0 > x180:0:0 && cons_1 = 1) The following rules are bounded: f832_in(x180:0:0, x181:0:0, c) -> f832_in(c1, x181:0:0, c2) :|: c2 = 1 && (c1 = x180:0:0 + 1 && c = 1) && (x181:0:0 > x180:0:0 && cons_1 = 1) ---------------------------------------- (18) YES